Related papers: Robustness via Diffractal Architectures
In this article, starting from a Gibbs capacity, we build a new random capacity by applying two simple operators, the first one introducing some redundancy and the second one performing a random sampling. Depending on the values of the two…
Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…
Sparse sensor arrays have attracted considerable attention in various fields such as radar, array processing, ultrasound imaging and communications. In the context of correlation-based processing, such arrays enable to resolve more…
The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
Robustness of spatial pattern against perturbations is an indispensable property of developmental processes for organisms, which need to adapt to changing environments. Although specific mechanisms for this robustness have been extensively…
We propose the first fractal frequency mapping, which in a simple form enables to replicate complex neuronal effects. Unlike the conventional filters, which suppress or amplify the input spectral components according to the filter weights,…
The permeability of two-dimensional fractures with self-affine fractal roughness is studied via analytic arguments and numerical simulations. The limit where the roughness amplitude is small compared with average fracture aperture is…
Functional connectivity estimates are highly sensitive to analysis choices and can be dominated by noise when the number of sampled time points is small relative to network dimensionality. This issue is particularly acute in fMRI, where…
This preliminary paper presents initial explorations in rendering Iterated Function System (IFS) fractals using a differentiable rendering pipeline. Differentiable rendering is a recent innovation at the intersection of computer graphics…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
Recurrence behavior of wave packets in coupled higher dimensional systems and periodically driven systems is analyzed, which takes place in the realm of higher coupling/modulation strength. We analyze the wave packet dynamics close to…
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of…
We investigate fracture toughness of architected interfaces and their ability to maintain structural integrity and provide stable damage propagation conditions beyond the failure load. We propose theoretical and numerical frameworks to…
We consider a plate made from an isotropic but brittle elastic material, which is used to span a rigid aperture, across which a small pressure difference is applied. The problem we address is to find the structure which uses the least…
The random layer thickness variations can induce a great deformation of the experimental reflection of broadband extreme ultraviolet multilayer. In order to reduce this influence of random layer thickness fluctuations, the multiobjective…
The eigenmodes of unstable canonical optical resonators possess fractal structure in their transverse intensity cross-sections [Karman et al., Nature 402, 138 (1999)]. In one particular plane, the magnified self-conjugate plane, this…
This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations…
Hybrid optical systems combining refractive and diffractive optical responses have the potential to support new types of optical behavior, but they are difficult to model and optimize due to the disparate spatial scales and physics…
Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter…